1. Field of the Invention
This invention relates to a simulation apparatus for a ferroelectric device, more specifically an apparatus for simulating dynamic characteristics of a circuit including a ferroelectric memory device.
2. Description of the Related Art
It is known that a ferroelectric device shows a hysteresis in a relation between applied voltages and polarization charges. The ferroelectric device can be used as an nonvolatile type semiconductor memory or other devices by utilizing the electric characteristic. In this connection, the hysteresis of the ferroelectric device need to be evaluated quantitatively in case of using the ferroelectric device to a memory or other circuits.
In order to evaluate the hysteresis of the ferroelectric device quantitatively, a method presented on the JAPANESE JOURNAL OF APPLIED PHYSICS Volume 30, Number 9B page 2384 to 2387 issued on September, 1991 as a "Simulations of Ferroelectric Characteristics Using a One-Dimensional Lattice Model" under the name of OMURA et. al. can be used.
The method uses a simulation model utilizing an overall free energy "f" defined as an equation shown in below, EQU f=.SIGMA..sub.n=1, N {.alpha./2.multidot.p.sub.n.sup.2 +.beta./4.multidot.p.sub.n.sup.4 +k/2.multidot.(p.sub.n -p.sub.n-1).sup.2 -p.sub.n.multidot.e}
In the equation, P.sub.n shows a dipole moment of the n th lattice, k is an interaction coefficient of atoms located adjacently, e means an electric field and the equation satisfies a condition of .alpha.&lt;0, .beta.&gt;0. Also, .alpha. can be shown in a numerical formula shown in below as a function of temperature T, EQU .alpha.=a(T-T.sub.0)
wherein a condition of a&gt;0 must be satisfied, and T.sub.0 shows the Curie temperature. In addition, an equation shown in below is the equation for defining symbols in the above equation calculating the simulation model utilizing the overall free energy "f",
.SIGMA..sub.n=1, N {X.sub.n }=X.sub.1 +X.sub.2 + . . . X.sub.N
The hysteresis of the ferroelectric device will be evaluated quantitatively in accordance with the overall free energy "f" thus calculated.
However, the simulation method described above has the following problems to be resolved. The equation shown in above which describes physical phenomena under atomic basis is used as the simulation model in the conventional simulation method. Therefore, it is not appropriate to use the equation for describing phenomena caused under electric basis. Also, complication of the equation make hard to understand the equation itself at sight. As a result, it is not-easy to use the simulation results on engineering basis such as circuit analysis or the like. In addition, a computer having higher processing capabilities is required when the equation is calculated by the computer because the equation itself is complicated.
Further, in order to increase an operation speed of the ferroelectric memory or similar devices, it is necessary to evaluate not only the hysteresis of the ferroelectric device quantitatively but also quantitatively evaluate dynamic characteristics of a circuit including the ferroelectric device such as transient responses. The simulation model described above can not be used for simulating the dynamic characteristics of the circuit on engineering basis because the calculation is too complex to carry out.